Problem: Simplify the following expression: $\dfrac{35k^2}{30k}$ You can assume $k \neq 0$.
$ \dfrac{35k^2}{30k} = \dfrac{35}{30} \cdot \dfrac{k^2}{k} $ To simplify $\frac{35}{30}$ , find the greatest common factor (GCD) of $35$ and $30$ $35 = 5 \cdot 7$ $30 = 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(35, 30) = 5 $ $ \dfrac{35}{30} \cdot \dfrac{k^2}{k} = \dfrac{5 \cdot 7}{5 \cdot 6} \cdot \dfrac{k^2}{k} $ $\phantom{ \dfrac{35}{30} \cdot \dfrac{2}{1}} = \dfrac{7}{6} \cdot \dfrac{k^2}{k} $ $ \dfrac{k^2}{k} = \dfrac{k \cdot k}{k} = k $ $ \dfrac{7}{6} \cdot k = \dfrac{7k}{6} $